\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{glucose.pdf} 
\caption{Glucose metabolism} \label{fig:glucose}
\end{figure}
Here we introduce our running example:  \emph{glucose regulation} in human body (Figure \ref{fig:glucose}). %as it is a familiar process and it shows that our model is not limited to genetic regulations but it may express other kinds of interactions. 
In the following, we are always referring to the process under normal circumstances in a healthy body.

Glucose regulation is a homeostatic process: \ie the rates of glucose in blood (\emph{glycemia}) must remain stable at what we call the equilibrium state. 
Glycemia is regulated by  two hormones: \emph{insulin} and  \emph{glucagon}. When glycemia rises (for instance as a result of the digestion of a meal), insulin  promotes the storing of glucose in muscles through the  glycogenesis process, thus decreasing the blood glucose levels. 
Conversely, when glycemia is critically low, glucagon  stimulates the process of glycogenolysis that increases the blood glucose level by transforming glycogen back into glucose.


We will focus on the assimilation of sweeteners: \ie sugars  or  artificial sweeteners such as aspartame. Whenever we eat something sweet either natural or artificial, the sweet sensation sends a signal to the brain (through \emph{neurotransmitters}) that in turns stimulates the production of insulin by pancreas. In the case of sugar, the digestion transforms food into nutrients (\ie glucose) that are absorbed by blood.
This way, sugar through digestion  increases glucose in blood giving the sensation of satiety. In case the income of glucose produces hyperglycemia,  the levels of glucose are promptly equilibrated by the intervention of insulin.
Unlike sugar, artificial sweeteners are not assimilated by the body, hence they do not increase the glucose levels in blood. Nevertheless  the insulin produced under the stimuli originated by the sweet sensation can cause the rate of glucose to drop engendering hypoglycemia. In response to that, the brain induces the  stimulus of \emph{hunger}. As a matter of fact this appears as an unwanted/toxic behavior, indeed the assimilation of food (even if it contains aspartame) should calm hunger and induce satiety, and not the opposite. 

This schema suggests that we should consider four  levels for glycemia: low, hunger, equilibrium and high. Likewise for insulin we assume three levels: inactive, low and high. All other actors involved in glucose regulation, have only two  levels (inactive or active).  
In this example, concerning the durations of reactions, all complementary ones such as production of insulin and glucagon,  take the same amount of time, the signal to the brain is the fastest, and the decay of  glycemia values are much longer than the digestion process. In the following sections, we will see how to model the glucose metabolism in \rnd and how to verify the unexpected behaviors of artificial sweeteners.

